Quasicircles and Bounded Turning Circles Modulo bi-Lipschitz Maps

Herron, David A and Meyer, Daniel (2010) Quasicircles and Bounded Turning Circles Modulo bi-Lipschitz Maps. Rev. Mat. Iberoamericana, 28 (3). pp. 603-630.

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Official URL: http://dx.doi.org/10.4171/rmi/687

Abstract

We construct a catalog, of snowflake type metric circles, that describes all metric quasicircles up to \bl\ equivalence. This is a metric space analog of a result due to Rohde. Our construction also works for all bounded turning metric circles; these need not be doubling. As a byproduct, we show that a metric quasicircle with Assouad dimension strictly less than two is bi-Lipschitz equivalent to a planar quasicircle.

Item Type:	Article
Additional Information:	30 pages, 3 figures, to appear in Rev. Mat. Iberoamericana
Uncontrolled Keywords:	math.CV, math.CV, math.MG, 30L10
Depositing User:	Symplectic Admin
Date Deposited:	18 Dec 2017 09:26
Last Modified:	27 Feb 2024 19:37
DOI:	10.4171/rmi/687
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3014261